Related papers: Large deviations for multidimensional state-depend…

Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is…

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…

To investigate the complex dynamics of a biological neuron that is subject to small random perturbations we can use stochastic neuron models. While many techniques have already been developed to study properties of such models, especially…

In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…

In this paper, we consider a class of reflected stochastic differential equations for which the constraint is not on the paths of the solution but on its law. We establish a small noise large deviation principle, a large deviation for short…

In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207-248] under which the solution of the stochastic…

Large deviation principles and related results are given for a class of Markov chains associated to the "leaves" in random recursive trees and preferential attachment random graphs, as well as the "cherries" in Yule trees. In particular,…

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…

We consider delay differential equations (DDE) that are on the verge of an instability, i.e. the characteristic equation for the linearized equation has one root as zero and all other roots have negative real parts. In presence of small…

We study perpetuities of a special type related to the size-biased distributions. Necessary and sufficient conditions of their existence and uniqueness are obtained. A crucial point in proving all results is a close connection between…

The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A…

Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail…

We establish a large deviation principle for a reflected Poisson driven SDE. Our motivation is to study in a forthcoming paper the problem of exit of such a process from the basin of attraction of a locally stable equilibrium associated…

The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…

In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…

The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is…

In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…

The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…